Oort's conjecture on direct sums of Newton polygons of curves
Oort's conjecture on direct sums of Newton polygons of curves
For , let be positive integers, let be symmetric Newton polygons of height , and let . Define to be the symmetric Newton polygon of height obtained by taking the union of the slopes of and , with the multiplicity of each slope equal to the sum of its multiplicities in and .
Oort's conjecture. If occurs on for , then occurs on .
This conjecture predicts that Newton polygons realized by curves can be combined through direct sum. The paper studies some cases of the conjecture, while the general assertion remains open.
Sources & referencesView supporting material
Primary source
Rachel Pries, “Some cases of Oort's conjecture about Newton polygons”, arXiv:2306.11080 (2024).
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